Assumption Of Equilibrium Research Articles

Addressing the Apparent Controversies Between the Contact Angle-Based Models for Estimation of Surface Free Energy: A Critical Review

The most popular contact angle (CA)-based approaches for determination of solid surface free energy (SFE) are considered: (i) single liquid methods, mainly of Neumann and Chibowski, (ii) the multiple liquids approach of Owens–Wendt–Rabel–Kaelble (OWRK), and (iii) van Oss-Chaudhury–Good (vOCG) acid–base model. Evaluations based on Neumann and Chibowski models agree between each other. Under the assumption of equilibrium “wet wetting” (i.e., presence of saturated precursor film ahead of the drop), the model of Chibowski transforms in Lipatov’s interfacial equilibrium rule, i.e., the Antonow rule derived for the ternary point solid–liquid–gas. Very good agreement is observed between single and multiple liquids models where OWRK/vOCG values can be viewed as a mean of the individual SFE adopted by the solid with each of the wetting probes. Both approaches (single and multiple liquids) can be used in conjunction to evaluate SFE dispersion and polar components and to elucidate hydrophobicity and hydrophilicity. The implementation of apparently fully non-polar liquids (diiodomethane, bromonaphthalene) in OWRK and vOCG is practically and theoretically suspect. CA-based estimates represent apparent SFE determined by the interactions of both the solid surface and the probing liquid, which are very useful to elucidate the energy, chemistry and dynamics of the solid surface.

Uncovering Below Cloud Rain‐Vapor Interactions During Tropical Rain Events Through Simultaneous and Continuous Real‐Time Monitoring of Rain and Vapor Isotopes

AbstractDue to limited water vapor measurements, vapor isotopes have been traditionally estimated under the assumption of isotopic equilibrium between rain and vapor below cloud base. However, recent advancements in analytical instruments allow more vapor isotopic measurements that have challenged this assumption. To enhance our understanding of rain‐vapor interactions below cloud base in tropical regions, we established an automated system to measure rain and vapor isotopes simultaneously and continuously in real time at minute intervals in Singapore. Among 324 rain events monitored from 2016 to 2019, 81% exhibited a substantial departure of rain and vapor isotopes from the expected equilibrium. This departure suggests that raindrop evaporation plays a larger role in determining their isotopes. The conclusion is supported by the generally lower slopes of the local meteoric water line. Seasonal variations in rain event characteristics indicate changing influences of rain‐vapor interactions: during monsoons, more frequent heavy rainfall maintains relatively high humidity below cloud base, favoring rain‐vapor isotopic equilibrium, whereas during inter‐monsoons, more light rain events lead to pronounced rain evaporation and larger isotopic differences. Furthermore, rain‐vapor interactions below cloud base significantly modulated their isotope evolution during individual events. As events progressed, reduced humidity favored evaporation, increasing rain isotope values and decreasing its d‐excess, whereas vapor isotope values decreased and its d‐excess increased. Our study introduces a new approach to capturing real‐time high‐resolution rain and vapor isotopes at minute intervals to understand the dynamics of rain‐vapor interactions below cloud base. Findings underscore the crucial role of these interactions in influencing rain and vapor isotopes during tropical rain events.

The influence of continuum lowering on the equilibrium composition of plasma: case study of laser-induced plasma on a WC–Cu target

Abstract Composition of plasma obtained by laser ablation of cermet WC-Cu is calculated under the assumption of local thermodynamical equilibrium. Special attention is paid to the effect of lowering the ionization potential, the influence of which in the Saha equations is reflected both through the exponential Boltzmann term and through the partition functions of atomic and ionic species present in the plasma. The effect on these two terms are separated and quantified. It has been shown that the correction of the partition functions due to the reduction of the ionization potential is of greater importance than the correction of Boltzmann term, at higher temperatures for atomic species. It is thus necessary for the precise determination of the plasma composition, especially at higher temperatures. The effect of lowering the ionization potential on different types of atoms as well as on different ionic states is analyzed. Тhe change of the partition function due to the lowering of ionization energy affects also the concentration of single charged ions in an amount comparable to the correction of the Boltzmann term.

High-dimensional Bayesian likelihood normalisation for CRESST's background model

Using CaWO4 crystals as cryogenic calorimeters, the CRESST experiment searches for nuclear recoils caused by the scattering of potential Dark Matter particles. A reliable identification of a potential signal crucially depends on an accurate background model. In this work, we introduce an improved normalisation method for CRESST's model of electromagnetic backgrounds, which is an important technical step towards developing a more accurate background model. Spectral templates based on Geant4 simulations are normalised via a Bayesian likelihood fit to experimental background data. Contrary to our previous work, no explicit assumption of partial secular equilibrium is required a priori, which results in a more robust and versatile applicability. This new method also naturally considers the correlation between all background components. Due to these purely technical improvements, the presented method has the potential to explain up to 82.7 % of the experimental background within [1 keV,40 keV], an improvement of at most 18.6 % compared to our previous method. The actual value is subject to ongoing validations of the included physics.

Existence condition for detonations in condensed explosives with pressure–temperature equilibrium models

Most engineering tools dealing with detonation waves in condensed explosives are based on the reactive Euler equations, which involve a thermodynamic closure based on temperature and pressure equilibrium conditions. Indeed, the reactant and the detonation products are assumed to evolve in mechanical and thermal equilibrium. Although the assumption of thermal equilibrium is physically questionable, the reactive Euler equations are used for convenience. This choice is supported by several reasons. When considering thermal equilibrium, the assessment of thermal exchanges between the reactant and the detonation products is simplified, as no exchange coefficient needs to be determined. Furthermore, the reactive Euler equations are in conservative form and the shock relations are well-defined. This model appears to be the simplest option for addressing detonations in condensed explosives. However, this simplicity has limitations and conceals a subtle difficulty that can lead to pathological detonations. The present contribution investigates this difficulty and presents a global exothermic condition to preserve exothermic detonations in the frame of temperature–pressure equilibrium flow models. This condition depends on the equations of state only. It is independent of the kinetics used to model the decomposition of the explosive. By meticulously selecting the thermodynamic parameters of the equations of state for the reactant and detonation products, pathological detonations are prevented, thereby maintaining a globally exothermic reaction consistent with the Zeldovich–von Neumann–Döring theory.

Insight into the relationship between similarity and the degree of equilibrium of contaminant release curves through numerical simulations

The assumption of local equilibrium, especially in test standards for assessing the leaching of hazardous substances from materials, is crucial for the use of test results and the robustness of testing. However, previous studies of contact time conditions in percolation test standard have evaluated equilibrium and robustness separately. Therefore, this study tests the assumption of local equilibrium in the up-flow percolation test, standardized as ISO 21268-3 in 2019, and discusses the relationship between the similarity of test results and degree of equilibrium. Thus, we conducted approximately 6000 numerical simulations in total with varying leaching parameters to determine breakthrough curves (BTCs) for the substances investigated by the test standard. The results showed that the two BTCs for the longest and shortest contact time conditions within the standard test were identical over a wide range of parameters, supporting the robustness of the standard test. Interestingly, identical BTCs occur in equilibrium or near-equilibrium and nonequilibrium leaching. This finding indicates the need to reconsider the conventional interpretation that equilibrium is reached when test results with different contact time conditions appear identical and encourages efforts to develop procedures to verify equilibrium leaching.

On the Nature of the C IV-bearing Circumgalactic Medium at z~1

This paper presents a detailed study of the physical properties of seven C IV absorbers identified at z_abs = 0.68-1.28 along the line of sight toward QSO PG 1522+101 (z_QSO = 1.330). The study leverages high-quality QSO spectra from HST COS and STIS, and Keck HIRES to resolve component structures and to constrain the gas density and elemental abundances of individual components. Under the assumption of photoionization equilibrium (PIE), five of the 12 C IV components require a mixture of high- and low-density phases to fully explain the observed relative abundances between low-, intermediate-, and high-ionization species. In addition, galaxy surveys carried out using VLT MUSE and Magellan LDSS3C are utilized to characterize the galaxy environments. The results of this analysis are summarized as follows: (1) no luminous galaxies (> 0.1 L*) are found within 100 kpc in projected distance from the C IV absorbers; (2) the C IV selection preferentially targets high-metallicity (near solar) and chemically-evolved gas (~ solar [C/O] elemental abundances) in galaxy halos; (3) the observed narrow line widths of individual C IV components, places a stringent limit on the gas temperature (< 5e4 K) and supports a photoionization origin; (4) additional local ionizing sources beyond the UV ionizing background may be necessary for at least one absorber based on the observed deficit of He I relative to H I; and (5) a PIE assumption may not apply when the gas metallicity exceeds the solar value and the component line width implies a warmer temperature than expected from PIE models.

Chemical composition of planetary hosts: C, N, and α-element abundances

Accurate atmospheric parameters and chemical composition of planet hosts play a major role in characterising exoplanets and understanding their formation and evolution. Our objective is to uniformly determine atmospheric parameters and chemical abundances of carbon (C), nitrogen (N), oxygen(O), and the alpha -elements, magnesium (Mg) and silicon (Si), along with C/O, N/O and Mg/Si abundance ratios for planet-hosting stars. In this analysis, we aim to investigate the potential links between stellar chemistry and the presence of planets. e tai Observatory telescope. The determination of stellar parameters was based on a standard analysis using equivalent widths and one-dimensional, plane-parallel model atmospheres calculated under the assumption of local thermodynamical equilibrium. The differential synthetic spectrum method was used to uniformly determine the carbon C(C2), nitrogen N(CN), oxygen O I magnesium Mg I, and silicon Si I elemental abundances as well as the C/O, N/O, and Mg/Si ratios. We analysed elemental abundances and ratios in dwarf and giant stars, finding that C/Fe O/Fe and Mg/Fe are lower in metal-rich dwarf hosts; whereas N/Fe is close to the Solar ratio. Giants show smaller scatter in C/Fe and O/Fe and lower than the Solar average C/Fe and C/O ratios. The (C+N+O) abundances increase with Fe/H in giant stars, with a minimal scatter. We also noted an overabundance of Mg and Si in planet-hosting stars, particularly at lower metallicities, and a lower Mg/Si ratio in stars with planets. In giants hosting high-mass planets, nitrogen shows a moderate positive relationship with planet mass. C/O and N/O ratios show moderate negative and positive slopes in giant stars, respectively. The Mg/Si ratio shows a negative correlation with planet mass across the entire stellar sample.

Laser Metal Deposition of Rene 80—Microstructure and Solidification Behavior Modelling

New developments in nickel-based superalloys and production methods, such as the use of additive manufacturing (AM), can result in innovative designs for turbines. It is crucial to understand how the material behaves during the AM process to advance the industrial use of these techniques. An analytical model based on reaction–diffusion formalism is developed to better explain the solidification behavior of the material during laser metal deposition (LMD). The well-known Scheil–Gulliver theory has some drawbacks, such as the assumption of equilibrium at the solid–liquid interface, which is addressed by this method. The solidified fractions under the Scheil model and the pure equilibrium model are calculated using CALPHAD simulations. A differential scanning calorimeter is used to measure the heat flow during the solid–liquid phase transformation, the result of which is further converted to solidified fractions. The analytical model is compared with all the other models for validation.

Jacobian-free Newton-Krylov method for multilevel nonlocal thermal equilibrium radiative transfer problems

Context. The calculation of the emerging radiation from a model atmosphere requires knowledge of the emissivity and absorption coefficients, which are proportional to the atomic level population densities of the levels involved in each transition. Due to the intricate interdependence of the radiation field and the physical state of the atoms, iterative methods are required in order to calculate the atomic level population densities. A variety of different methods have been proposed to solve this problem, which is known as the nonlocal thermodynamical equilibrium (NLTE) problem. Aims. Our goal is to develop an efficient and rapidly converging method to solve the NLTE problem under the assumption of statistical equilibrium. In particular, we explore whether the Jacobian-Free Newton-Krylov (JFNK) method can be used. This method does not require an explicit construction of the Jacobian matrix because it estimates the new correction with the Krylov-subspace method. Methods. We implemented an NLTE radiative transfer code with overlapping bound-bound and bound-free transitions. This solved the statistical equilibrium equations using a JFNK method, assuming a depth-stratified plane-parallel atmosphere. As a reference, we also implemented the Rybicki & Hummer (1992) method based on linearization and operator splitting. Results. Our tests with the Fontenla, Avrett and Loeser C model atmosphere (FAL-C) and two different six-level Ca II and H I atoms show that the JFNK method can converge faster than our reference case by up to a factor 2. This number is evaluated in terms of the total number of evaluations of the formal solution of the radiative transfer equation for all frequencies and directions. This method can also reach a lower residual error compared to the reference case. Conclusions. The JFNK method we developed poses a new alternative to solving the NLTE problem. Because it is not based on operator splitting with a local approximate operator, it can improve the convergence of the NLTE problem in highly scattering cases. One major advantage of this method is that it is expected to allow for a direct implementation of more complex problems, such as overlapping transitions from different active atoms, charge conservation, or a more efficient treatment of partial redistribution, without having to explicitly linearize the equations.

Calculation of thermodynamic properties and transport coefficients of Ar/N2–H2–Si plasma

Abstract The composition, thermodynamic properties and transport coefficients of Ar – H 2 – Si and N 2 – H 2 – Si plasma within a temperature range of 300–30 000 K and pressure range of 0.1–10 atm are calculated under the assumptions of local thermal equilibrium (LTE) and local chemical equilibrium (LCE). Taking Debye–Hückel corrections into account, the chemical equilibrium composition and thermodynamic properties of these two plasma systems are derived using the mass action law and classical statistical thermodynamics respectively. The transport coefficients, including viscosity, conductivity, and thermal conductivity, are calculated using the Chapman–Enskog (C–E) method extended to a third-order approximation (second-order for viscosity and heavy particle translational thermal conductivity). Some of the results have been compared with those of other researchers, and there is a good level of agreement. The slight difference arises from the selection of interaction potential. The final calculation reveals that the introduction of silicon vapor significantly alters the thermodynamic properties and transport coefficients of Ar / N 2 – H 2 – Si plasma, even at a small concentration of silicon vapor (1%), the effect on the electrical conductivity cannot be ignored. Furthermore, our calculation results provide the fundamental data for numerical simulations of magnetohydrodynamics (MHD) for the synthesis of silicon nanoparticles and silicon composites.

Non-equilibrium thermal models of lithium batteries

Temperature fluctuations impact battery performance, safety, and health. Industry-standard cell-level models of these phenomena ignore thermal gradients within the electrodes’ active material, i.e., assume the latter to be in “thermal equilibrium”. We present a “non-equilibrium” thermal model that explicitly accounts for spatial variability of temperature with the active material (and the carbon-binder domain). We investigate the conditions, expressed in terms of the heat-generation rate and the thermal properties of a cell’s liquid (electrolyte) and solid (active material and CBD) phases, under which the thermal equilibrium assumption breaks down and our model should be used instead. The differences between these two thermal models are investigated further by coupling them with an industry-standard electrochemical model. The resulting thermal–electrochemical model demonstrates the importance of thermal gradients within the active material at high C-rates (discharge current densities) and for large grain sizes. Under these conditions, the equilibrium assumption underestimates internal temperature by as much as 50%. These two thermal models are then applied to a commercial NMC battery with multiple units. Our non-equilibrium model predicts the battery surface temperature that is in good agreement with measurements, while the equilibrium model underestimates the observed temperature.

Climate covariate selection influences MaxEnt model predictions and predictive accuracy under current and future climates

The performance and transferability of species distribution models (SDMs) depends on a number of ecological, biological, and methodological factors. There is a growing body of literature that explores how the choice of climate covariate combinations and model parameters can affect predictive performance, but relatively few that delve into covariate reduction methods and the optimisation of model parameters, and the resulting spatial and temporal transferability of those models. The present work used the citrus pest, Diaphorina citri Kuwayama (Hemiptera: Psyllidae), to illustrate how MaxEnt models trained on the insect’s native range in Asia varied in their predictions of climatic suitability across the introduced range when eight different covariate reduction methods were applied during model building. Additionally, it showed how model sensitivity varied across these different covariate combinations using three sets of independently validated occurrence points in the invaded range of the psyllid. Climatically suitable areas for D. citri differed by as much as two-fold between the best and worst-performing models in selected areas. Great care should be taken in the selection of the highest-performing predictor combinations and model parameter settings for SDMs, particularly in the case of invasive species where the assumption of environmental equilibrium is likely violated in the introduced range. Understanding how the predictive ability of SDMs can be influenced by the methodological choices made during the model building phase is vital to ensuring that ecological and invasion management programmes do not over- or underestimate climatic suitability and subsequent invasion risk.

Large/small eddy simulations: A high-fidelity method for studying high-Reynolds number turbulent flows

Direct numerical simulations (DNS) are one of the main ab initio tools to study turbulent flows. However, due to their considerable computational cost, DNS are primarily restricted to canonical flows at moderate Reynolds numbers, in which turbulence is isolated from the realistic, large-scale flow dynamics. In contrast, lower fidelity techniques, such as large eddy simulations (LES), are employed for modeling real-life systems. Such approaches rely on closure models that make multiple assumptions, including turbulent equilibrium, small-scale universality, etc., which require prior knowledge of the flow and can be violated. We propose a method, which couples a lower-fidelity, unresolved, time-dependent calculation of an entire system (LES) with an embedded small eddy simulation (SES) that provides a high-fidelity, fully resolved solution in a sub-region of interest of the LES. Such coupling is achieved by continuous replacement of the large SES scales with a low-pass filtered LES velocity field. The method is formulated in physical space, with no assumptions of equilibrium, small-scale structure, and boundary conditions. A priori tests of both steady and unsteady homogeneous, isotropic turbulences are used to demonstrate the method's accuracy in recovering turbulence properties, including spectra, probability density functions of the intermittent quantities, and sub-grid dissipation. Finally, SES is compared with two alternative approaches: one embedding a high-resolution region through static mesh refinement and a generalization of the traditional volumetric spectral forcing. Unlike these methods, SES is shown to achieve DNS-level accuracy at a fraction of the cost of the full DNS, thus opening the possibility to study high-Re flows.

Fate of initially bound timelike geodesics in spherical boson stars

Boson stars are horizonless compact objects and they could possess novel geodesic orbits under the equilibrium assumption, which differ from those in black hole backgrounds. However, unstable boson stars may collapse into black holes or migrate to stable states, resulting in an inability to maintain the initially bound geodesic orbits within the backgrounds of unstable boson stars. To elucidate the fate of initially bound geodesic orbits in boson stars, we present a study of geodesics within the spherical space times of stable, collapsing, and migrating boson stars. We focus on timelike geodesics that are initially circular or reciprocating. We verify that orbits initially bound within a stable boson star persist in their bound states. For a collapsing boson star, we show that orbits initially bound and reciprocating finally either become unbound or plunge into the newly formed black hole, depending on their initial maximal radii. For initially circular geodesics, we have discovered the existence of a critical radius. Orbits with radii below this critical value are found to plunge into the newly formed black hole, whereas those with radii larger than the critical radius continue to orbit around the vicinity of the newly formed black hole, exhibiting nonzero eccentricities. For the migrating case, a black hole does not form. In this case, the reciprocating orbits span a wider radial range. For initially circular geodesics, orbits with small radii become unbound, and orbits with large radii remain bound with nonvanishing eccentricities. This geodesic study provides an approach to investigating the gravitational collapse and migration of boson stars. Published by the American Physical Society 2024

Action-based dynamical models of M31-like galaxies

ABSTRACT In this work, we present an action-based dynamical equilibrium model to constrain the phase-space distribution of stars in the stellar halo, present-day dark matter distribution, and the total mass distribution in M31-like galaxies. The model comprises a three-component gravitational potential (stellar bulge, stellar disc, and a dark matter halo), and a double power-law distribution function (DF), $f(\mathbf {J})$, which is a function of actions. A Bayesian model-fitting algorithm was implemented that enabled both parameters of the potential and DF to be explored. After testing the model-fitting algorithm on mock data drawn from the model itself, it was applied to a set of three M31-like haloes from the Auriga simulations (Auriga 21, Auriga 23, and Auriga 24). Furthermore, we tested the equilibrium assumption and the ability of a double power-law DF to represent the stellar halo stars. The model incurs an error in the total enclosed mass of around 10 per cent out to 100 kpc, thus justifying the equilibrium assumption. Furthermore, the double power-law DF used proves to be an appropriate description of the investigated M31-like haloes. The anisotropy profiles of the haloes were also investigated and discussed from a merger history point of view, however, our approach underscores to capture the non-equilibrium anisotropy information of stellar haloes in Auriga models, which is expected.

Multi-cycle Direct Numerical Simulations of a Laboratory Scale Engine: Evolution of Boundary Layers and Wall Heat Flux

AbstractMulti-cycle direct numerical simulations (DNS) of a laboratory-scale engine at technically relevant engine speeds (1500 and 2500 rpm) are performed to investigate the transient velocity and thermal boundary layers (BL) as well as the wall heat flux during the compression stroke under motored operation. The time-varying wall-bounded flow is characterized by a large-scale tumble vortex, which generates vortical structures as the flow rolls off the cylinder wall. The bulk flow is found to strongly affect the development of the BL profiles, especially at higher engine speeds. As a result, the large-scale flow structures lead to alternating pressure gradients near the wall, invalidating the flow equilibrium assumptions used in typical wall modeling approaches. The thickness of the velocity BL and of the viscous sublayer was found to scale inversely with engine speed and crank angle. The thermal BL thickness also scales inversely with engine speed but increases with in-cylinder temperature. In contrast, thermal displacement thickness, which is sometimes used as a proxy for thermal BL thickness, was found to decrease with increasing temperature in the bulk. Examination of the heat flux distribution revealed areas of increased heat flux, particularly at places characterized by strong flow directed towards the wall. In addition, significant cyclic variations in the surface-averaged wall heat flux were observed for both engine speeds. An analysis of the cyclic tumble ratio revealed that the cycles with lower tumble ratio values near top dead center (TDC), indicative of an earlier tumble breakdown, also exhibit higher surface averaged wall heat fluxes. These findings extend previous numerical and experimental results for the evolution of BL structure during the compression stroke and serve as an important step for future engine simulations under realistic operating conditions.

Modelling and simulation on compressible multi-component gas-liquid flows with chemical reaction and phase transition effects

In this paper, mathematical models and numerical algorithm are conducted for simulating compressible two-phase multi-component reactive flows, coupling with the finite-rate-based chemistry and the instantaneous-equilibrium phase transition model. Distinctive from previous multi-component two-phase governing equations, all volume fraction transport equations, with non-conservative characteristics, of gaseous components are substituted with a thermal equilibrium assumption inside the gaseous mixture for closure. Moreover, based on the temperature polynomial (NASA-7) fitted gas properties and the stiffened gas equation of state (SG-EOS) described liquid properties, the instantaneous-equilibrium phase transition model is re-derived, and the solving strategy of the transient phase transition model is detailly provided using an algebraical approach rather than the iterative process. Having included these elements, the proposed model is validated on three canonical tests, first for pure reactive flows, second for pure two-phase flows, and third for complex compressible multi-component two-phase reactive flows with phase transition effects: hydrogen-oxygen detonation interacting with a water droplet. The cases have well demonstrated the proposed model capability and the expected fluid physics in both the multiphase and reactive flows are reproduced.

Bridging Model–Data Discrepancies in Mars’ Dayside Ionosphere: Exploring Varying Reaction Rate Coefficients

Measurements of concentrations of neutral and ion species in the upper atmosphere of Mars by the Neutral Gas and Ion Mass Spectrometer (NGIMS) on board the Mars Atmosphere and Volatile EvolutioN mission have served as model input and/or for comparison with model output in numerous earlier studies of the Martian dayside ionosphere. While many models reproduce the altitudinal density profiles of key ion species within a factor of a few, it has proven challenging to achieve a level of agreement within tens of percent for multiple ion species over a wide range of altitudes. We explore means to overcome this issue while keeping with a reduced chemical model and utilizing the assumptions of photochemical equilibrium and that the NGIMS data are devoid of any measurement errors. We entertain, for instance, the idea that the rate coefficient for the charge-transfer reaction between CO2+ and O may vary with altitude as a result of a pressure-controlled internal energy distribution of the CO2+ population.

Going beyond an old shockwave conjecture for improving upon Navier-Stokes.

Nonequilibrium molecular dynamics (NEMD) computer simulations of steady shockwaves in dense fluids and rarefied gases produce detailed shockwave profiles of mechanical and thermal properties. The Boltzmann equation, under the assumption of local thermodynamic equilibrium (LTE), leads to the first-order (linear) continuum theory of hydrodynamic flow: Navier-Stokes-Fourier (NSF). (Expansion of the LTE Boltzmann equationin higher powers of gradients yields so-called Burnett second-order terms, etc.) NEMD simulations of strong shockwaves with high gradients are not well modeled by NSF theory. Many years ago, a conjecture for going "beyond Navier-Stokes" was proposed, applying the empirical observation of anisotropic thermal enhancement in the shock front to the temperature dependence of the NSF transport coefficients, whose dissipation determines the slope at the center of the shock profile: for weak shocks, the actual coefficients in NEMD simulations appear to be smaller than in NSF predictions, leading to steeper gradients being observed, while for strong shocks, the NEMD coefficients appear to be larger, leading to less steep shock rises than predicted by NSF calculations. In this paper, we show that adding significant Burnett nonlinearity into an LTE continuum theory reproduces the early shock rise and slope of NEMD profiles, for both weak and strong shocks in dense fluids, as well as strong shockwaves in the ideal gas. Moreover, we show that "Holian's conjecture" incorporates significant Burnett nonlinearity, but like all the other LTE continuum theories, it fails to describe the slow NEMD return to equilibrium beyond the shock front. We show that Maxwell relaxation has to be applied to the hydrodynamic variables themselves (rather than attempting indirect relaxation of their gradients) in order to more accurately model the entire shockwave profile. Non-LTE Maxwell relaxation is the only way to bring the entire profile into agreement with NEMD, most noticeably for strong shockwaves.